#28 NormalityTest,shapiro_wilk_pvalue works incorrectly?

[Anonymous]

Hi,
I just started to use JDistlib to calculate normality.
It calculates W with NormalityTest.shapiro_wilk_statistic(x) as it is supposed to.
But when I try to calculate p-value using NormalityTest,shapiro_wilk_pvalue(w,x.length) the result is different than I expected.
E.g. for n=10 and W=0.842 p-value should be around 0.05 (according to S-W tables like http://www.real-statistics.com/wp-content/uploads/2012/12/image3742.png)
but
NormalityTest.shapiro_wilk_pvalue(0.842, 10) returns p=3.3858759941785735E-48
Interestingly for n=10:
w=0.90 p=9.366645710023918E-12
w=0.95 p=0.9999199643824663

Could you explain how it works (if it is not a bug)?
Thanks in advance - BTW I find your library very helpful and simple to use,

[Roby Joehanes]

Hi there. Thanks! Could you please give me an example dataset?

[Roby Joehanes]

Perhaps to give you more information, I translated the algorithm from R directly. R used algorithm AS R94 (See Royston 1995):

https://stat.ethz.ch/R-manual/R-devel/library/stats/html/shapiro.test.html

I did a quick check on how it performs and the output matches exactly with R. If you suspect that there is a bug, then it could very well be R's bug. This is why I need the exact example dataset so that I can report back to R maintainers.

The table you referenced might be taken from an older algorithm.

[Roby Joehanes]

Forget about what I just said. It is indeed a bug. Fixed in version 0.4.4. Thank you so much!

[Roby Joehanes]

Test case JDistlib:

double[] n2 = c(0.139, 0.157, 0.175, 0.256, 0.344, 0.413, 0.503, 0.577, 0.614, 0.655, 0.954, 1.392, 1.557, 1.648, 1.690, 1.994, 2.174, 2.206, 3.245, 3.510, 3.571, 4.354, 4.980, 6.084, 8.351);
w = NormalityTest.shapiro_wilk_statistic(n2);
p = NormalityTest.shapiro_wilk_pvalue(w, n2.length);
System.out.println(w + " -- " + p);

Test case R:

n2 <- c(0.139, 0.157, 0.175, 0.256, 0.344, 0.413, 0.503, 0.577, 0.614, 0.655, 0.954,
 1.392, 1.557, 1.648, 1.690, 1.994, 2.174, 2.206, 3.245, 3.510, 3.571, 4.354,
 4.980, 6.084, 8.351)
  sw <- shapiro.test(n2);
  sw$statistic;
  sw$p.value;

Correct w = 0.8346663
Correct p-value = 0.0009134905

[Anonymous]

Thank you! Now it works perfectly :)